Bounds of singular sets for elliptic equations in C^{1, Dini} domains with singular potentials

@misc{wang2026bounds,
  title = {{Bounds of singular sets for elliptic equations in $C^1, Dini$ domains with singular potentials}},
  author = {Zhiwei Wang and Jiuyi Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.21988},
  eprint = {2609.21988},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21988},
}

TY  - UNPB
TI  - Bounds of singular sets for elliptic equations in C^1, Dini domains with singular potentials
AU  - Zhiwei Wang
AU  - Jiuyi Zhu
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.21988
UR  - https://arxiv.org/abs/2609.21988
AB  - We study the quantitative codimension-two estimate for the singular set in the boundary neighborhoods of the solutions of Δu+V(x)u=0 in Ω, u=0 on ∂Ω, where Ω⊂ℝ^n is a bounded C^1,Dini domain and V∈ L^p(Ω) for some p>n. We first prove the explicit upper bound for the doubling index is given by C(n,p,Ω)(1+|V|_L^p(Ω)^2p/(3p−2n)).The analytic input is an interior volume estimate for solutions of second order elliptic equations with uniformly elliptic Dini leading coefficients and V∈ L^p. Using the quantitative doubling index bound, boundary flattening, we show an explicit upper bound for singular sets in the neighborhood of the boundary of the C^1,Dini domain.
ER  -